Ultrasound technology is commonly used as part of diagnostic or inspection tools in a range of industries including medicine, foodstuffs, pharmaceuticals, petrochemicals, chemicals and materials processing. Such tools produce characterization of data in a non-invasive or non-destructive fashion. In known ultrasound methods, ultrasounds are transmitted to scatterers in a medium and backscattered or scattered echoes are detected. Ultrasound parameters such as backscattering coefficient, angular scattering, attenuation, speed of sound, material nonlinearity and statistics can then be used to reveal intrinsic material properties of the scatterers or the medium such as microstructure and/or composition.
In ultrasound imaging of biological tissues, the ultrasound signal backscattered by the components of the tissue has been used to extract quantitative properties of the scatterers to reveal properties such as the correlation length of structures composing the medium. This method and the other aforementioned approaches have been used successfully to detect and diagnose medical conditions, such as prostate cancer, early Duchenne muscular dystrophy, cell apoptosis and carcinomas.
However, these methods are not suitable for all applications. They are particularly unsuitable for characterizing dense concentrations of scatterers in a medium such as dense suspensions of particles or cells. It is desirable to obtain quantitative information regarding the physical dimensions of such scatterers. For example, in two-phase systems such as solid particles/droplets of insoluble liquid/gas bubbles in a fluid, it is desirable to quantitatively characterize the suspensions in terms of the suspended particle size, concentration and other physical parameters.
One such application is in medical diagnostics where the aggregation of red blood cells is known to be an independent risk factor of circulatory related disorders such as thrombosis, atherosclerosis and valvular heart disease. Red blood cell aggregation is also a surrogate marker of inflammation. Furthermore, the presence and size of circulating embolisms in the blood vessels of a patient can be indicative of their risk of suffering a stroke or a coronary artery ischemic syndrome.
For years, many investigators have attempted to quantify the ultrasound backscatter from blood by analyzing the power spectra of the radio frequency (rf) echoes to estimate the aggregation level of red blood cells (RBCs). The aim is to detect abnormal RBC aggregation and its pathophysiological impact on associated circulatory diseases, namely, deep venous thrombosis, atherosclerosis, and microcirculatory flow disorders such as in diabetes mellitus. The hypothesis is that ultrasound blood characterization techniques can provide in vivo and in situ evaluation of RBC aggregation for diagnostic purposes.
Two quantitative ultrasonic parameters that have been proven useful for blood characterization are the backscattering coefficient (BSC) and the spectral slope (SS). The BSC is defined as the differential backscattering cross section per unit volume and the SS is the linear slope of the BSC as a function of frequency on a log-log scale. In most numerical and in vitro experimental studies, the BSC increases and the SS decreases as the level of aggregation increases.
Ultrasound backscattering by blood is mainly due to RBCs that constitute a major portion of the blood cellular content. Blood can thus be described as a biphasic fluid composed of RBCs immersed in plasma at a volume concentration (i.e., a systemic hematocrit) typically varying between 30 and 50%. The high cellular number density of blood induces destructive wave interferences and a nonlinear backscattered power versus hematocrit relationship.
In the absence of aggregation, a few stochastic scattering models were proposed to better understand the ultrasound backscattered power properties. Two classical approaches are known as the particle and continuum models. The particle model (PM) consists of summing contributions from individual RBCs, all considered much smaller than the acoustic wavelength, and modeling the RBC interaction by an analytical packing factor expression. The continuum model (CM) considers that scattering arises from spatial fluctuations in the density and compressibility of the blood continuum. In a hybrid model generalizing the PM and CM frameworks, the RBCs are treated as a single scattering unit within a voxel, which size is defined as a fraction of the acoustic wavelength. The contribution from each single scattering unit is then determined as in the PM, and the contribution from all voxels is then summed by considering the influence of the mean number of scatterers per voxel and its variation in numbers between voxels. The framework of the hybrid model was generalized and the structure factor model (SFM) was introduced for the case of non-aggregating RBCs.
A major difficulty for modeling blood backscattering is to consider clustering particles as RBC aggregates. The aforementioned approaches are valid in the Rayleigh scattering regime (i.e., for a product of the wavenumber k times the scatterer radius a, ka<<1), which is characterized by a fourth-order frequency dependence (spectral slope SS=4), whereas the SS for aggregated RBCs differs from the fourth power law. Accordingly, Savery and Cloutier (“A point process approach to assess the frequency dependence of ultrasound backscattering by aggregating red blood cells,” J. Acoust. Soc. Am., vol. 110, No. 6, pp. 3252-3262, 2001) proposed the SFM to predict backscattering by aggregating RBCs at a low hematocrit. This model was later generalized to a normal hematocrit of 40% (Fontaine, Savery and Cloutier, “Simulation of ultrasound backscattering by red blood cell aggregates: effect of shear rate and anisotropy”, Biophysical Journal, vol. 82, pp. 1696-1710, 2002). The SFM sums the contributions from individual RBCs and models the RBC interaction by a statistical mechanics structure factor, which is by definition the Fourier transform of the spatial distribution of RBCs. It is important to emphasize that the low frequency limit of the structure factor is by definition the packing factor used under Rayleigh scattering conditions, and that the structure factor cannot analytically be calculated contrary to the packing factor. To estimate the aggregate structure parameters by fitting the measured BSC to a modeled BSC, the SFM would be computationally intensive because of the various possible RBC spatial distributions that would need to be estimated for statistical robustness, under both normal and pathological aggregating conditions. Yu et al. (“Experimental ultrasound characterization of red blood cell aggregation using the structure factor size estimator,” J. Acoust. Soc. Am., vol. 122, No. 1, pp. 645-656, 2007; “Ultrasonic parametric imaging of erythrocyte aggregation using the structure factor size estimator,” Biorheology, vol. 46, pp. 343363, 2009) recently developed a scattering theory, called the structure factor size estimator (SFSE), that approximates the SFM by using a second-order Taylor expansion of the structure factor. The SFSE parameterizes the BSC by two structure indices: the packing factor and mean aggregate diameter assumed to be isotropic. However, experiments with pig blood in controlled flow devices and three-dimensional numerical simulations of isotropic aggregates showed that the two indices may follow a quadratic relationship, reducing the BSC parameterization to one parameter.
With current existing SFSE technology, one can acquire ultrasound RF data from a blood vessel, estimate the backscatter coefficient BSC over the frequency bandwidth of acquired data, fit a BSC model as a function of frequency to the experimental BSC data, and estimate the packing factor and mean aggregate size. With such state-of-the-art, one can obtain parametric cellular images of RBCs and RBC aggregates flowing within blood vessels. Those images can then be used for the abovementioned applications, for example the diagnosis of blood circulatory disorders and quantification of the inflammatory response of a disease. None of these prior art techniques allows the measure of the compactness of the RBC aggregates. Also, the bias resulting from the use of these methods needs to be reduced in order to provide a more accurate characterization of the RBC aggregates. There is therefore a need for a new imaging method providing additional physical parameters describing the structure of flowing RBC aggregates with better accuracy than the above mentioned methods.